Machines for forming and filling dunnage units from sheets of plastic are known. Machines which produce dunnage units by inflating preformed pouches in a preformed web are also known. For many applications, machines which utilize preformed webs are preferred.
Typically, the entire length of sides of adjacent dunnage units formed from a preformed web are connected by perforations. In prior art webs, these perforations extend all the way to an inflation edge of the web.